The greatest whole number, by which the expression n4 +

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The greatest whole number, by which the expression n⁴ + 6n³ +11n² + 6n + 24 is divisible for every natural number n, is

1. 6
2. 24
3. 12
4. 48

Correct Option: D

For n = 1
n⁴ + 6n³ +11n² + 6n + 24
⇒ n⁴ + 6n³ +11n² + 6n + 24 = 1 + 6 + 11 + 6 + 24 = 48
For n = 2
n⁴ + 6n³ +11n² + 6n + 24 = 16 + 48 + 44 + 12 + 24
⇒ n⁴ + 6n³ +11n² + 6n + 24 = 144 , which is divisible by 48.
Clearly, 48 is the required number.